I’ll put it this way, if Pink Diamond we’re to say “Pearl, I ORDER you to do such and such…” because she’s her Pearl, she would have to do it. Of course her servant mentality played a role in her allegiance to Rose, how could it not. BUT, that relationship clearly grew and changed as naturally as any relationship will, and it wasn’t due to Pink Diamonds powers or influence.
Have no fear, Pearl is her own gem and wasn’t being puppet controlled by Pink/Rose her whole life. It’s not mind control.